Berger, N, Procaccia, EB and Turner, A orcid.org/0000-0002-6015-5392 (2022) Growth of stationary Hastings–Levitov. Annals of Applied Probability, 32 (5). 5. pp. 3331-3360. ISSN 1050-5164
Abstract
We construct and study a stationary version of the Hastings–Levitov(0)(0) model. We prove that, unlike in the classical HL(0)(0) model, in the stationary case the size of particles attaching to the aggregate is tight, and therefore SHL(0)(0) is proposed as a potential candidate for a stationary off-lattice variant of diffusion limited aggregation (DLA). The stationary setting, together with a geometric interpretation of the harmonic measure, yields new geometric results such as stabilization, finiteness of arms and arm size distribution. We show that, under appropriate scaling, arms in SHL(0)(0) converge to the graph of Brownian motion which has fractal dimension 3/23/2. Moreover we show that trees with n particles reach a height of order n2/3n2/3, corresponding to a numerical prediction of Meakin from 1983 for the gyration radius of DLA growing on a long line segment.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 Institute of Mathematical Statistics. This is an author produced version of an article published in Annals of Applied Probability. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 10 Nov 2022 14:18 |
Last Modified: | 10 Nov 2022 14:18 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Identification Number: | 10.1214/21-AAP1761 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:193014 |